Comparison of a Finite Element Method and a Finite Volume Method for Flow on General Grids in 3D

H. Haegland (1) , I. Aavatsmark (1) , Cindy Guichard (2, 3) , Roland Masson (4, 5) , R. Kaufmann (1)

1 UiB - University of Bergen
2 LJLL - Laboratoire Jacques-Louis Lions
3 ANGE - Numerical Analysis, Geophysics and Ecology
4 COFFEE - COmplex Flows For Energy and Environment
5 LJAD - Laboratoire Jean Alexandre Dieudonné

We compare the recently developed Vertex Approximate Gradient (VAG) scheme developed in [R. Eymard et al., ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 2012] and the multipoint flux approximations (MPFA) O- and L-methods on 3D irregular meshes. It is found that the VAG scheme converges for a wider range of problems than the MPFA methods, however when the MPFA-methods converge, the convergence rate in flux is better than for the VAG method.

Domaines: Analyse numérique [math.NA]

H. Haegland, I. Aavatsmark, Cindy Guichard, Roland Masson, R. Kaufmann. Comparison of a Finite Element Method and a Finite Volume Method for Flow on General Grids in 3D. ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, Sep 2012, Biarritz, France. ⟨10.3997/2214-4609.20143222⟩. ⟨hal-01238554⟩